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Section 8C Real Population Growth

Section 8C Real Population Growth. pages 536 - 546. Population Growth Patterns. Linear Growth occurs when a population increases by the same absolute amount in each unit of time. Example: Straightown -- 500 each year

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Section 8C Real Population Growth

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  1. Section 8CReal Population Growth pages 536 - 546

  2. Population Growth Patterns Linear Growthoccurs when a population increases by the same absolute amount in each unit of time. Example: Straightown -- 500 each year Exponential Growthoccurs when a population increases by the same relative amount (same percentage) in each unit of time. Example: Powertown: -- 5% each year Real Population Growthassumes a varying growth rate from year to year.

  3. ex1/537 The average annual growth rate for world population since 1650 has been about 0.7%. However the annual rate has varied significantly. It peaked at about 2.1% during the 1960s and is currently (2006) about 1.2%. a) Find the approximate doubling time for each of these growth rates. b) Predict the world population in 2050 based on the 2000 population of 6.0 billion. Predicted 6E9 (1+.007)50 Populations: 6E9 (1+.021)50 6E9 (1+.012)50 Doubling 70/0.7Times 70/2.1 70/1.2

  4. 23/544 Predict the world population in 2050 based on a 2000 population of 6.0 billion. Use the average annual growth rate between 1850 and 1950 which was about 0.9%. 25/544 Predict the world population in 2050 based on a 2000 population of 6.0 billion. Use the average annual growth rate between 1970 and 2000 which was about 1.6%.

  5. Population Growth Rates The world population growth rate is the difference between the birth rate and the death rate: growth rate = birth rate – death rate National population growth rates are more complicated. Why?

  6. ex2/538 In 1950, the world birth rate was 3.7 births per 100 people and the world death rate was 2.0 deaths per 100 people. By 1975, the birth rate had fallen to 2.8 births per 100 people and the death rate was 1.1 deaths per 100 people. Contrast the growth rates in 1950 and 1975. 1950: 3.7/100 – 2.0/100 = .017 = 1.7% 1975: 2.8/100 – 1.1/100 = .017 = 1.7% Overall growth rates are the same.

  7. 29/545 Find Sweden’s net growth rate due to births and deaths (i.e. neglect immigration) in 1985, 1995 and 2003. 1985: 11.8/1000 – 11.3/1000 = .0005 = .05% 1995: 11.7/1000 – 11.0/1000 = .0007 = .07% 2003: 11.0/1000 – 10.0/1000 = .001 = 0.1% Varying growth rates are most realistic!

  8. Logistic Population Growthpg 539 Logistic Growthassumes that population growth gradually slows as the population approaches the carrying capacity (i.e. the maximum sustainable population). The growth rate is given by: where r is the base growth rate.

  9. If the population is small, the growth rate is close to the base growth rate. As the population grows, the growth rate becomes smaller. If the population hits the carrying capacity, then growth rate is zero.

  10. S – shaped curve Population approaches the carrying capacity and levels off.

  11. 31/545 Consider a population that begins growing exponentially at a base rate of 4.0% per year and then follows a logistic growth pattern. If the carrying capacity is 60 million, find the actual growth rate when the population is 10 million, 30 million, and 50 million.

  12. Homework : Pages 544-545 # 24*,26*,28, 32 *Use EXACT formula based on given info.

  13. Common Logarithms (page 531) log10(x) is the power to which 10 must be raised to obtain x. log10(x) recognizes x as a power of 10 log10(x) = y if and only if 10y = x log10(1000) = 3since103 = 1000. log10(10,000,000) = 7since 107 = 10,000,000. log10(1) = 0since 100 = 1. log10(0.1) = -1since10-1 = 0.1. log10(30) = 1.4777since101.4777 = 30. [calculator]

  14. Common Logarithms (page 505)

  15. Practice with Logarithms (page 506) 13/506 100.928 is between 10 and 100. 15/506 10-5.2 is between 100,000 and 1,000,000. 17/506is between 0 and 1. 19/506 log10(1,600,000) is between 6 and 7. 21/506 log10(0.25) is between 0 and 1.

  16. Properties of Logarithms (page 531) log10(x) is the power to which 10 must be raised to obtain x. log10(x) recognizes x as a power of 10 log10(x) = y if and only if 10y = x log10(10x) = x log10(xy) = log10(x) + log10(y) log10(ab) = b x log10(a) Practice (page 533)

  17. Properties of Logarithms (page 505)

  18. Homework : Page 533 # 24,26,28,32,34

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